Getting Around

Wednesday, April 10, 2013

Introducing Slope

line by geogebra
We are working on graphing right now and it's time to do slope. I hated, Hated, HATED slope when I was in middle school. Rise over run made no sense to me at all. I thought about how to approach slope this year for weeks.

Usually I start with a line that's got points on it, I do the whole rise over run business, and we plug away until we can do it without too many errors. Eventually I take away the pre-plotted points and they have to come up with those.

Since one of our standards is that students will be able to draw a line given two points or a point and a slope, I decided to start by drawing this time. Once we had a line with two points down I gave them one point and asked what I'd need to know to draw a particular line.

They thought about it. I love this. They really thought about it. At one point someone suggested that we needed to know how to get to the next point so we'd know what direction to go in. Brilliant! So I told them to go 2 up and 3 over (to the right, because right now we're always reading graphs left to right). I wrote 2/3 as a ratio with the words "up" and "over" next to the numbers. Then, on a new coordinate plane, I drew the same starting point but with different "clues" to the next point. And then another one. And another one. And then I let them tell me how to find the next point on the line.

This could have flopped in so many ways, particularly since this class has many behavioral issues. But it worked!

What I love is that THEY figured out that the top number is related to y somehow. THEY decided that we could skip the word "down" and slap a negative sign on there. THEY noticed that 3/2 gets you the same line as 6/4.

I only barely brought up the word slope toward the end of class. I briefly mentioned rise over run, but didn't dwell on it. Their whole assignment was to take points and slopes I gave them and graph them for practice. I plan to do more practice in class tomorrow before we start finding slopes on lines that have already been drawn. I'm thinking I might make it a treasure-map sort of activity, or one where one kid comes up with the slope from a line and passes it to another kid who has to draw the original line based on what the first kid gave them.

While I have no expectations that they will understand slope better than students who learned with me before, I really loved trying something new and having it work out so well. I wish class could be like that everyday!

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